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Lab Assignment 7: Circular Motion

Instructor’s Overview

Circular motion is an integral part of our everyday lives. We experience circular motion when we leave highways on cloverleaf exits and on amusement park rides. Countless systems and devices leverage circular motion. We will discuss real-world applications in this module’s discussion. In this lab, you will directly experiment with uniform circular motion and quantify the behavior of a simple system. To execute the lab, you’ll synthesize your knowledge and experience with free-body diagrams and Newton’s second law.

In this lab, you will create a simple system of two different masses connected by a piece of fishing line. Here’s the twist: The fishing line is threaded through a tube. You will rotate the tube and achieve an equilibrium situation where the lower mass is vertically stationary. You will then use your knowledge of circular motion to analyze the situation.

This activity is based on Lab 8 of the eScience Lab kit.

Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations.

Experiment Tips:

Make sure you use fishing line instead of string for the experiment. Can you guess why?

Be careful when you rotate the mass. Be aware of your surroundings so nothing is inadvertently hit by the rotating mass.

Enlist the aid of a partner to time your experiments. Date: Student: Abstract Introduction

Material and Methods Results

Data table:

*Complete this column after performing the calculation in question 5 below.Based on your results from the experiment, please answer the following

questions:

Drawacircletorepresentthepathtakenbyyourrotatingmass.Placea dot on the circle to represent your rotating washer. Add a straight line from the dot to the center of the circle, representing the radius of rotation (the string). Now label the direction of the tangential velocity and the centripetal force.

Hereisadiagramofourexperimentalsituation:

Radius (meters)

Time for 15 revs

Period (sec)

Theoretical Period (sec)*

0.25

0.40

0.15

Please add vectors to create a free-body diagram. Assume that m1 is rotating at a speed v with a constant radius R.

The following forces should be included in your free-body diagram:

Tension in the string

Centripetal force on the rotating mass

Gravitational force on the hanging mass Hint: Each mass experiences the tension in the string. The string tension ultimately cancels out when you solve Newton’s equations of motion for both masses.

Fromyourfree-bodydiagram,writethesumoftheforcesexperiencedby mass m1. From your free-body diagram, write the sum of the forces experienced by mass m2. (For the equation for mass m1, use the following relations to replace the speed, v: v = ωR, where R is the radius of rotation ω = 2π/T, where T is the period of rotation.) In question 4 you will solve the two above equations to obtain the period of the rotating system in terms of the radius of rotation and the two masses, m1 and m2.

Solvetheaboveequationfortheperiod,T.

Now let’s look at the special case of our experiment: 4m1 = m2. Show that our general expression for the period T becomes: Using this expression for the period, fill in the theoretical period in the results table.

Howdidtheperiodofrotationvaryasyouchangedtheradius?Howdoes the angular frequency change?

7. Wereyourexperimentalvaluesclosetothetheoreticalvalues?Howcould you improve the experiment to reduce error?

Conclusions

References

April 14, 2021